The two men smiled at each other as they shook hands in front of the world's press for several seconds and exchanged words in a packed hall as the prince toured the National University of Ireland Galway.

The Queen and the Duke of Edinburgh at Mountbatten's funeral in Westminster Abbey

After their meeting, Mr Adams told reporters: "I think it was a good meeting.

"We discussed the need for the entire process to move forward in terms of people who have suffered, families who have been bereaved, and the need to heal.

"To have relationships between the people of these islands and of this island, moving toward the future."

Prince Charles told him he had reflected on his own suffering which the royal said had "given him an affinity and understanding of other people," Mr Adams added.

Prince Charles with Mountbatten

Charles and the Duchess of Cornwall's visit to the university is the first engagement on a four-day visit.

It is move which would have been unthinkable until a few years ago, and sets the tone for the trip, the theme of which is reconciliation.

Security was tight around the university as the royal couple arrived.

They touched down on a chartered flight at Shannon Airport in Co Clare earlier this morning before travelling to Galway city for the first stop in a packed agenda, with two days of engagements planned on either side on the Irish border.

Mr Adams is the most senior republican to meet the Prince and it comes after his party colleague Martin McGuinness, the Northern Ireland Deputy First Minister and former IRA commander, shook hands with Charles at a state banquet in Windsor Castle last year and met the Queen in 2012.

Charles is due to go on an emotional walkabout in the seaside village of Mullaghmore, Co Sligo, where Lord Mountbatten was killed.

He was targeted by the IRA as he set off with family and a local teenager to gather lobster pots and fish for shrimp 600 yards from the harbour of the normally peaceful fishing village.

Lord Mountbatten died along with Lady Doreen Brabourne, the 83-year-old mother-in-law of the earl's daughter, his 14-year-old grandson Nicholas Knatchbull, and 14-year-old Paul Maxwell, from Killynur, Enniskillen.